DG discretization of optimized Schwarz methods for Maxwell's equations

El Bouajaji, Mohamed and Dolean, Victorita and Gander, Martin J. and Lanteri, Stéphane and Perrussel, Ronan (2014) DG discretization of optimized Schwarz methods for Maxwell's equations. In: Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, 98 . Springer-Verlag, pp. 217-225. ISBN 9783319057897

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    We study here optimized Schwarz domain decomposition methods for solving the time-harmonic Maxwell equations discretized by a discontinuous Galerkin (DG) method. Due to the particularity of the latter, a discretization of a more sophisticated Schwarz method is not straightforward. A strategy of discretization is shown in the framework of a DG weak formulation, and the equivalence between multi-domain and single-domain solutions is proved. The proposed discrete framework is then illustrated by some numerical results through the simulation of two-dimensional propagation problems.